Degrees ↔ Radians Converter
Convert between degrees, radians and gradians. Live as you type, with the exact formula shown. Free, runs in your browser.
The conversion formulas
Degrees → radians: rad = deg × π / 180
Radians → degrees: deg = rad × 180 / π
The fraction-of-π form is often cleaner: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 360° = 2π.
Frequently Asked Questions
How do you convert degrees to radians?
Multiply by π / 180. Since a full circle is 360° = 2π radians, one degree is π/180 ≈ 0.0174533 radians. Example: 45° × π/180 = 0.7854 rad.
How do you convert radians to degrees?
Multiply by 180 / π. One radian is 180/π ≈ 57.2958°. Example: 1 rad × 180/π = 57.2958°.
Why do programmers and mathematicians use radians?
Radians make calculus and many trig formulas cleaner — for example, sin(x) ≈ x for small x only works when x is in radians. Most programming languages (JS, Python, C) accept radians in their sin/cos/tan functions, not degrees.
What about gradians (gons)?
A gradian (or gon) divides a right angle into 100 units, so a full circle is 400 grad. It is used in surveying in some European countries. To convert: grad = deg × 10/9, or grad = rad × 200/π. This tool includes a gradian output for completeness.